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Grand Junction sends a signal to Radon’s GPS. What kind of signal? Grand Junction Transmitter Radon in Boulder it puts the time on the signal. For this to work, we’ll need for both the transmitter and Radon to have clocks. GPS

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When Radon’s GPS receiver gets the signal, he compares the time on the signal with the time on his clock. So, a GPS signal tells you how far you are from the transmitter. Time Difference (in seconds) * 2.99792458 10 8 meters/second = Distance (in meters)

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If the distance from the GPS transmitter is 250 miles, that means you are somewhere on a circle of radius 250 miles.

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And a third transmitter in Pueblo Radon is at the intersection of the 3 circles

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This only works if: You know where the transmitters are. GPS signals also transmit the satellite locations. Everyone has good clocks. The GPS satellites have very good clocks. A GPS user can use a 4th signal to piggy-back onto the GPS satellite clocks. And you can tell the transmitters apart. The signals are made in a way so that you can tell which transmitter sent them. For real problems, we use the intersection of three spheres, not three circles.

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When GPS receives a signal It compares that signal with all the known codes (there are currently 37). The receiver determines which satellite it is. It decodes the timing information, multiplies by the speed of light to find the radius of the sphere. Once it has done that for 3 satellites, it can determine the location.

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How do GPS signals send all this information? They use codes! Binary codes. Each satellite has a different code.

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Strategy First we need to learn how GPS creates these codes Then we need to come up with a way to quickly tell the codes apart.

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How do you create codes? You use binary addition rules. 0+0=0 1+0=1 0+1=1 1+1=10 (but only use the last bit, 0) GPS uses “shift registers.” The more shift registers you have, the more complicated you can make your code.

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Register1Register2Register3Code 111- Start with all 1’s in your shift registers Add Register 1 and Register 3 The answer 0 goes into Register 1 and everything shifts to the right. Here is an example with 3 shift registers For this example, 1+1 =10 ==> 0

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01100010101011001000100100000110000011110000 11000101010110010001001000001100000111100001 01100010101011001000100100000110000011110000 11000101010110010001001000001100000111100001 Agreement is perfect But if you recognize they are shifted by 1: This example: same satellite codes, but shifted Not so good - score of -3.

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It’s useful to have a computer to do these comparisons, especially since you have to test a lot of different shifts. Then you can plot how good the agreement is as a function of shift.